Pseudoboundaries of spaces \(\lambda X, NX, GX, GrX\) (Q1812843)

Let \(X\) be a compact space, and let \(\exp X\) denote its hyperspace consisting of all nonempty closed subsets. The author considers several natural subspaces \(Z\) of \(\exp(\exp X)\) that were previously known to be homeomorphic to the Hilbert cube \(Q\) and proves that for natural subsets \(E\) of \(Z\) the pairs \((Q,B)\) and \((Z,E)\) are homeomorphic. Here \(B\) denotes the pseudo-boundary of \(Q\).